Reims striker Boulaye Dia put the visitors ahead after five minutes at Stade Louis II. Then things got even worse when forward El Bilal Touré dribbled to the edge of the area and beat goalkeeper Benjamin Lecomte with a fine shot.
“We made mistakes early in the game,” Kovač said. “But we showed very good fitness and a lot of motivation for the next 70 minutes.”
Defender Axel Disasi pulled a goal back against his former club in first-half stoppage time, and fellow center half Benoît Badiashile equalized in the 55th from Russia midfielder Aleksandr Golovin’s free kick.
Monaco dominated possession thereafter but could not find a winner.
Gouiri gave coach Patrick Vieira’s Nice the cutting edge.
The 20-year-old Frenchman was signed from Lyon for 7 million euros ($8.3 million) and showed the kind of ability that saw him finish top scorer at the under-17 European Championship in 2017.